The Random Phase Approximation for Interacting Fermi Gases in the Mean-Field Regime

Martin Ravn Christiansen, Christian Hainzl, Phan Thành Nam

Published 2021-06-21Version 1

We present a general approach to justify the random phase approximation for the homogeneous Fermi gas in three-dimensions in the mean-field scaling regime. We consider a system of $N$ fermions on a torus, interacting via a two-body repulsive potential proportional to $N^{-\frac{1}{3}}$. In the limit $N\rightarrow\infty$, we derive the exact leading order of the correlation energy of the system, which coincides with the prediction of Gell-Mann and Brueckner in 1957.